Semi-Implicit Variational Inference

TL;DR

Semi-implicit variational inference (SIVI) introduces a flexible variational family by mixing parameters with arbitrary distributions, enabling more accurate posterior inference that approaches MCMC performance.

Contribution

SIVI expands variational inference by allowing implicit distributions and provides a novel optimization method with bounds on the evidence lower bound.

Findings

SIVI closely matches MCMC accuracy in posterior inference.

SIVI's bounds facilitate effective stochastic optimization.

Flexible variational distributions improve inference quality.

Abstract

Semi-implicit variational inference (SIVI) is introduced to expand the commonly used analytic variational distribution family, by mixing the variational parameter with a flexible distribution. This mixing distribution can assume any density function, explicit or not, as long as independent random samples can be generated via reparameterization. Not only does SIVI expand the variational family to incorporate highly flexible variational distributions, including implicit ones that have no analytic density functions, but also sandwiches the evidence lower bound (ELBO) between a lower bound and an upper bound, and further derives an asymptotically exact surrogate ELBO that is amenable to optimization via stochastic gradient ascent. With a substantially expanded variational family and a novel optimization algorithm, SIVI is shown to closely match the accuracy of MCMC in inferring the posterior in a variety of Bayesian inference tasks.